A concrete strip footing with a width of B is founded at the depth of D_f, below the surface of a level site. The water table is at a depth of D_w below the ground surface. The soil at the site consists of clay having the following properties:  

The soil total unit weight = g_t,   the undrained cohesion = c_u, the undrained friction angle = f_u, the drained cohesion = c′ and the drained friction angle = f′

Use Hansen’s theory of bearing capacity to determine the allowable bearing pressure, which could be placed on the footing assuming a factor of safety of F for the following cases:

1. Immediately after loading the footing
2. 
   
3. Long time after loading the footing
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5. Plot a graph with two curves to show the variation of the allowable bearing pressures with the total unit weight of soil ranging from 15 kN/m³ to 21 kN/m³ in drained and undrained conditions.
6. Plot a graph with two curves to show the variation of the allowable bearing pressures with the depth of footing ranging from D_f  = 0 to D_f  = 2.5B in drained and undrained conditions. Notes: The load is vertical and uniformly distributed over the footing. The ground and the base of footing are horizontal. D_f should be less than or equal to 2.5 B. The variable D_w can be positive or zero (zero means the water table is at the ground surface). Assume the water level cannot be above the ground surface. For the sake of simplicity, assume that the total unit weights of soil above and below the water table are the same.